3) Elsie, a librarian wants to investigate the length of time, 7 minutes, that people spent in her library on a particular day. Elsie's data for 160 people who visited the library on that particular day is shown in the following table. T (minutes) Frequency 0≤T<20 50 20≤T<40 0 10 62 20 Elsie assumes her data to be representative of future visitors to the library. The following box and whisker diagram shows the times, in minutes, that the 10 visitors spent in the library. 30 40 ≤ T < 60 k 40 60 50 T (minutes) 60 ≤ T < 80 14 70 80 a) State whether the variable T is discrete or continuous. b) Find the value of k. c) 90 80 ≤ T < 100 8 100 Elsie believes the box and whisker diagram indicates that the times spent in the library are not normally distributed. i) Write down the modal class. ii) Write down the mid-interval value for this class. d) Use Elsie's data to calculate an estimate of the mean time that people spent in the library. e) Using the table, write down the maximum possible number of people who spent 35 minutes or less in the library on that day. f) Find the probability a visitor spends at least 60 minutes in the library. g) Write down the median time spent in the library. h) Find the interquartile range. Hence show that the longest time that a person spent in the library is not an outlier